CAMELS Multifield Dataset (CMD) Analysis - Final Project Guideline

Course: Physics 434 - Data Analysis Lab
Dataset: CAMELS Multifield Dataset for Cosmological Simulations

Introduction

The CAMELS Multifield Dataset (CMD) is a suite of cosmological simulations designed to train machine learning models for extracting cosmological information from observational data. This notebook introduces you to real cosmological simulation data analysis using:

• Dark Matter Simulations: N-body simulations with varying cosmological parameters
• Hydrodynamic Simulations: Full galaxy formation physics including stellar feedback
• Multifield Maps: 2D projections of dark matter, gas density, temperature, and stellar mass
• Parameter Variations: Systematic exploration of Ωm, σ8, and astrophysical parameters

Dataset Access: https://camels-multifield-dataset.readthedocs.io/en/latest/ The CMD provides thousands of simulation realizations with known cosmological parameters, making it ideal for statistical analysis and parameter estimation studies.

Learning Objectives

If you choose this dataset for your final project, by the end, you will understand:

1. Cosmological simulation data structure and multifield analysis
2. Maximum likelihood estimation for parameter inference
3. Chi-squared analysis and likelihood surface mapping
4. Monte Carlo sampling techniques for uncertainty quantification
5. Statistical significance testing and cut optimization methods
6. Advanced data analysis techniques for astronomical datasets

Final Project Options Available

1. Cosmological Parameter Estimation - MLE and likelihood surface analysis
2. Model Selection and Validation - Chi-squared tests and information criteria
3. Monte Carlo Parameter Inference - MCMC sampling and uncertainty propagation
4. Signal Detection and Optimization - Significance testing and cut optimization
5. Statistical Reweighting - Histogram reweighting and systematic uncertainty analysis
6. Multi-Parameter Likelihood Analysis - Joint parameter constraints and degeneracies

Your final output for parameter estimation can look like this (from CAMELS paper):

Recommended Project Guidelines and Next Steps

Available Final Projects

Based on this CMD dataset, you can think about the following questions or design your own project, e.g. play around with the 2D data with different parameter labels, you can reference this tutorial.

Cosmological Parameter Estimation via Maximum Likelihood

Recommended Steps:

1. Load CMD simulation maps with known cosmological parameters (Ωm, σ8) and extract statistical measures like power spectra or correlation functions.
2. Calculate theoretical predictions for these statistics as a function of cosmological parameters using fitting functions or interpolation.
3. Implement maximum likelihood estimation to constrain cosmological parameters from mock observational data with realistic noise.
4. Use chi-squared minimization and profile likelihood methods to map likelihood surfaces and determine parameter constraints.
5. Generate confidence contours and error ellipses for joint parameter constraints using likelihood ratio tests.
6. Compare results across different astrophysical feedback models (IllustrisTNG, SIMBA) to assess systematic uncertainties.
7. Validate parameter recovery using Monte Carlo simulations and assess bias in estimators.
8. Interpret results in the context of current cosmological tensions and survey capabilities.

Model Selection and Validation in Cosmological Simulations

Recommended Steps:

1. Extract multifield maps (dark matter, gas, stellar mass) from CMD simulations with varying astrophysical parameters.
2. Calculate cross-correlation statistics between different fields as a function of simulation parameters.
3. Implement information criteria (AIC, BIC) to compare different theoretical models for field correlations.
4. Use chi-squared goodness-of-fit tests to validate model predictions against simulation data.
5. Perform cross-validation analysis by training on subset of simulations and testing on independent realizations.
6. Generate model comparison plots showing relative likelihoods and evidence ratios between competing theories.
7. Assess systematic uncertainties from baryonic physics using controlled parameter variations.
8. Interpret model selection results for understanding galaxy formation physics and cosmological inference.

Monte Carlo Parameter Inference and Uncertainty Quantification

Recommended Steps:

1. Load CMD datasets spanning the full cosmological parameter space and extract summary statistics -- power spectrum.
2. Implement Markov Chain Monte Carlo (MCMC) sampling to explore posterior distributions for cosmological parameters.
3. Use emulator techniques (Gaussian processes, neural networks) to interpolate simulation predictions across parameter space.
4. Generate posterior samples and compute credible intervals using appropriate MCMC diagnostics and convergence tests.
5. Analyze parameter degeneracies and correlations through corner plots and covariance matrix analysis.
6. Implement importance sampling and reweighting techniques to combine different simulation suites.
7. Validate MCMC results using independent sampling methods and assess chain convergence.
8. Compare Bayesian and frequentist approaches to parameter estimation and uncertainty quantification.

Getting Started with Your Project

1. Choose your project based on your interests in cosmology and statistical complexity preference
2. Use this notebook as your starting point - copy relevant analysis frameworks
3. Download CMD data from the official repository following documentation guidelines
4. Implement the specific methods outlined in your chosen project using cosmological analysis tools
5. Validate your results using the statistical techniques and simulation-based tests

Required Deliverables (All Projects)

• Analysis notebook with clear explanations of cosmological context and well-commented code
• Publication-quality visualizations with proper error bars, confidence regions, and statistical information
• Statistical validation of your results using appropriate hypothesis tests and uncertainty quantification
• Cosmological interpretation connecting your statistical results to fundamental physics and survey science
• Discussion of systematic uncertainties and comparison with current observational constraints

Resources for Success

• CMD Documentation: https://camels-multifield-dataset.readthedocs.io/ - Comprehensive guide to dataset structure and usage
• Cosmological Analysis Tools: astropy.cosmology, CCL, CAMB/CLASS for theoretical predictions
• Statistical Libraries: scipy.stats, emcee, getdist for parameter estimation and MCMC analysis
• Simulation Analysis: nbodykit, Corrfunc for correlation function and power spectrum calculations
• CAMELS Papers: For methodology validation and comparison with published results
  • CAMELS project overview: https://arxiv.org/abs/2010.00619
  • CMD paper: https://arxiv.org/abs/2109.10915
  • Cosmological parameter estimation: https://arxiv.org/abs/2109.10360

Additional Analysis Tools for Advanced Projects

Consider these specialized packages for cosmological analysis:

• Power spectrum estimation: nbodykit.algorithms.FFTPower, Corrfunc.theory
• Parameter estimation: emcee.EnsembleSampler, dynesty.NestedSampler
• Emulator construction: sklearn.gaussian_process, george, GPy
• Statistical analysis: getdist.plots, chainconsumer for posterior visualization
• Data handling: h5py, numpy.memmap for efficient large dataset processing

Good luck with your cosmological data analysis project! 🌌